However, most of existing results focused on LDS with deterministic dynamics. The reason comes from two aspects: (i) deterministic system is easily analyzed; (ii) deterministic LDS can be modelled as a linear-like system by algebraic state space method using STP. From a technical point of view, there are three key points in the process of modeling deterministic LDS into its algebraic formulation: projection, swap, and descending power, which are implemented by projection operator, swap operator, and power-reduced operator, respectively. Inspired by the successful application of algebraic formulation to deterministic LDSs, some researchers attempt to apply it to stochastic LDSs [1]}-[2]}. However, when we shift our attention to LDS with stochastic dynamics, power-reduced operator is not applicable any more. Therefore, it is difficult to obtain the algebraic formulation of LDS with stochastic dynamics.
The intrinsic cause of the difference in the modeling of deterministic LDS and stochastic LDS is that the latter is inherently non-linear.
